Work

Multilayer crisscross error and erasure correction

Year: 2025

Type: article

Abstract: In this work, multilayer crisscross error and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are derived, including a Singleton bound, and maximum multi-cover distance (MMCD) codes are defined as those attaining it. Duality, puncturing and shortening of linear MMCD codes are studied. It is shown that the dual of a linear MMCD code is not necessarily MMCD, and those satisfying this duality condition are defined as dually MMCD codes. Finally, some constructions of codes in the multi-cover metric are given, including dually MMCD codes, together with efficient decoding algorithms for them.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2025.09.014

Author: Umberto Martínez-Peñas

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funders: European Commission, Ministerio de Ciencia e Innovación, Universidad de Valladolid

Awards: G2420222995, G3406072781, G6144962946